Abstract

Deterministic earthquake scenario simulations are playing an increasingly important role in seismic hazard and risk estimation. The numerical calculation of the complete 3D wavefield in the observed frequency band for a seismically active basin remains a computationally expensive task. This expense restricts seismologists either to calculating source models with homogeneous media (e.g., Gallovic and Brokesoová, 2004, 2007a,b), or to calculating single source scenario in 3D media (e.g., Olsen and Archuleta, 1996; Olsen, 2000; Ewald et al., 2006) while the complex effects of the media and the source on the ground motion are getting more and more attention. At the same time, with the development of the instrument, ground rotation introduced by an earthquake becomes a more and more important topic. Our aim is to provide a tool with which we can calculate a large number of different finite-source scenarios for a particular fault or fault system located in a 3D structure which will enable us to estimate ground motion (translation and rotation) variations due to source and 3D structure. In order to avoid having to run numerical expensive 3D code for each kinematic source scenario we propose the concept of “numerical Green’s functions” (NGF): a large seismic fault is divided into sub-faults of appropriate size for which synthetic Green’s functions at the surface of the seismically active area are calculated and stored. Consequently, ground motions from arbitrary kinematic sources can be simulated for the whole fault or parts of it by superposition.
To demonstrate the functionalities of the method a strike-slip NGF data base was calculated for a simplified vertical model of the Newport-Inglewood fault in the Los Angeles basin. As a first example, we use the data base to estimate variations of surface ground motion (e.g., peak ground velocity (PGV)) due to hypocentre location for a given final slip distribution. The results show a complex behavior, with dependence of absolute PGV and its variation on asperity location, directivity effect and local under-surface structure. Hypocentral depth may affect peak ground velocity in a positive or negative way depending on the distance from the fault and the receiver location with respect to basin structure.
Finite-fault source inversions reveal the spatial complexity of earthquake slip over the fault plane. In this study, several possible earthquake scenarios of Mw 7.0 are simulated with different quasi-dynamic finite source models for the Newport-Inglewood fault in the Los Angeles basin. We investigate the effects of the various slip histories on peak ground velocities and the related variations in ground motion prediction for our study area. The results confirm that the fault perpendicular components of motion are dominated by directivity effects while the fault parallel component is influenced both by the slip distribution and the basin structure. There are theoretical considerations suggesting that observations/calculations of the rotation part of earthquake-induced ground motions may provide additional information for earthquake risk hazard analysis after reports on rotational effects on structures (like twisting of tombstones or statues). For the first time, we carry out a systematic study of earthquake scenario simulations in 3D media with a specific focus on the rotational part of the motions. We simulate several M7 earthquakes with various hypocentre locations and slip histories on the Newport-Inglewood fault embedded in the 3D Los Angeles Basin. We investigate source
and basin structure effects on the rotational components of ground motion (e.g., peak ground rotation rates and their variation, horizontal gradients) and compare with the effects on translations.
Igel et al. (2005) shows a similarity of the observed waveforms between transverse acceleration and the vertical rotation rate in the teleseismic range benefiting from the recently developed ring laser instruments. The vertical rotation rate is found to be surprisingly similar to the horizontal translations in waveform which is explained with the plane wave propagation in the global range. That condition could not be hold any more in the near-field range, but some information could be extracted from the comparison between the translations and the rotation rate. As a final application, we investigate the source-dependent variations on rotational ground motions and compare with the results for translations.
The thesis is structured as follows:
Chapter 1: An insight into the present standard procedures carried out in the Seismic Hazard Assessment (SHA) is shown and then the different methodologies for predicting ground motions are described and compared, which are working individually or cooperate with each other. In recent years, one of those methods – deterministic calculations have been used widely and its consumption both in terms of CPU time and memory motivated the development of one new tool. We name that tool Numerical Green’s Function (NGF) method.
Chapter 2: An introduction to the different solutions of the wave propagation is given and the state-of-the-art technologies are described. We will introduce in detail the techniques adopted. We show how to implement the source, how to solve the wave propagation problem, and how to efficiently absorb the energies outgoing from the working area, or reflect them at the free surface boundary. To correctly account for the rupture process, which has been found to be the most important contributor to the ground motion in the near-source region, different tools are developed which can be divided into two groups: kinematic description and dynamic description of the source. These two descriptions are briefly compared. Then we focus on the “quasi-dynamic” method developed by Guatteri et al. (2004) which combines, to some extent, the two different approaches. This method is used to provide us the rupture processes we will
consider.
Chapter 3: Green’s function stands for the response on the surface due to an impulse dislocation at the source. A large earthquake rupture can be represented with a group of impulse dislocations, and thus the ground motion on the surface can be achieved by the superposition of its Green’s functions. In this chapter, we follow the representation theorem published in Aki and Richards (2002) to give the theoretical basis of that method and briefly describe the two groups of that method: composite method and integral method. Finally we introduce our new method – Numerical Green’s Function, present the basic equations and analyze its relationship with the representation theorem and empirical Green’s function
method.
Chapter 4: Discretization of the fault plane into elements and assumption the source parameters identical inside each element will introduce errors in the calculated seismic motions and these errors are expected to depend on some few parameters such as the fault geometry, the rupture velocity, the sub-fault size, the cut-off frequency for low-pass filtering the ground motions, the directivity effect, etc.. In this chapter we design a hypothetic velocity structure
and investigate how the errors introduced by the fault discretization will change with those parameters. The results are considered to provide some clues for our next step – selecting a seismic active fault and discretizing it into pieces with optimal sizes for which the Green’s functions will be calculated and stored.
Chapter 5: The working area of this study, the Newport Inglewood fault embedded in the Los Angeles basin is introduced. The Los Angeles basin is chosen as our working area because of the high seismicity and that the most reliable information about the subsurface structure could be achieved. One active fault, the Newport-Inglewood fault inside this region is considered as a possible place where an M7.4 earthquake could happen in the future decades. Also its near vertical straight fault plane facilitates the implementation of this fault into the finite difference method. After choosing the fault and velocity structure, we re-address the optimal size of sub-fault by simulating a few M7 earthquakes and investigate the peak ground velocity and the waveform difference introduced by the different discretizations.
The importance of the directivity effect on the ground motion in the near-source region has been recognized and is one of the main targets of the next generation of the attenuation relationship. A brief introduction to the physics of wave propagation is given in order to make the following discussions and illustrations of our results understandable for readers without previous knowledge. We analyze the different directivity effect supposed to happen between different component, or different kinds of motion (translation and rotation).
Chapter 6: This chapter addresses the problem of the variations of surface ground motion (e.g., peak ground velocity) due to hypocentre location for a given final slip distribution. A complex behavior about the dependence of absolute PGV and its variation on asperity location, directivity effect and local structure is presented. Hypocentral depth may affect PGV in a positive or negative way depending on the distance from the fault and the location with respect to the basin structure. The directivity effect is found to control the seismic motion generation for a specific final slip distribution.
Chapter 7: Inversions of the spatial and temporal evolution of earthquake slip on fault planes provide compelling evidence that fault displacement is spatially variable at all resolvable scales. Investigations of strong ground motion also indicate the spatial variability of the rupture velocity. This source physics complexity appeals for thorough description of the source process when calculating seismic motion. The method developed before hand allows efficient simulation of arbitrary slip histories. In this chapter, we investigate how the various slip histories affect peak ground velocities and the related variations in ground motion prediction for our study area. The fault perpendicular components of motion are confirmed to be dominated by directivity effects while the fault parallel component is influenced both by the slip distribution and the basin structure.
Chapter 8: The rotational motions excited by earthquakes are believed to be capable of providing more information for the aim of earthquake hazard analysis. But to the present time, those information are hard to be acquired. The first reason is that the spacing of the accelerograph recording sites is too large to get the indirect rotational motion measurement from the accelerograph recordings. The second reason is that the small amplitude of the rotational motion is beyond the recording capability of the present instruments. At the present time, the answers lie in the numerical simulation. In this section, for an M7.0 earthquake which is considered to happen on the Newport-Inglewood fault embedded in the Los Angeles basin, different parameters responsible for the ground rotation variation, like the hypocentre location, directivity effect and slip history, are systematically investigated. In the teleseismic range where plane wave assumption can be made, Igel et al. (2005) investigates the relationship between the translation and the rotation in terms of the amplitude ratio and waveform similarity. In this section, we find the waveform similarity between one horizontal acceleration and the vertical rotation rate even in the near-source region. We also calculate the amplitude ratio between the acceleration and the rotation rate and compare the results with the medium properties. That ratio is found to be somehow correlative to the basin depth.
Chapter 9: The most important results in this work are briefly summarized. Future promising prospectives are also described.
Appendix A: The individual peak ground velocity distributions corresponding to the varying hypocentres of the grid presented in chapter 6 are presented as a table for better illustration in case of interest. Three components of velocity and rotation rates are summarized here.
Appendix B: The peak ground velocity distributions are grouped into different tables corresponding to the varying slip histories (chapter 7). Three components of velocity and rotation rate are summarized here.